Positive Steady-State Solutions of a Competing Reaction-Diffusion System with Large Cross-Diffusion Coefficients

Abstract

This paper deals with a coupled system of reaction-diffusion equations modeling the competition of two species with cross diffusion. We discuss the existence of positive steady-state solutions in relation to the intrinsic birth ratesa1,a2of species and the cross diffusion coefficients β12,β21. Our results show that positive steady-state solutions exist ifa1anda2lie in certain range, or if β12and β21are sufficiently large.